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Answer: When backtesting using a two-tailed 90% confidence level test, there is a smaller probability of incorrectly rejecting a 95% VaR model than a 99% VaR model.
## Explanation This question deals with the statistical properties of VaR backtesting when switching from 95% to 99% confidence levels. **Key Concepts:** - **Type 1 Error**: Rejecting a correct model (false positive) - **Type 2 Error**: Accepting an incorrect model (false negative) - **Backtesting**: Comparing actual trading outcomes with VaR estimates **Analysis of Options:** **Option A**: Incorrect - The reliability of backtesting decisions depends on the statistical power of the test, not necessarily on the VaR confidence level itself. **Option B**: Incorrect - A 95% VaR model actually has a higher probability of being incorrectly rejected because it has more expected exceptions (5% vs 1% for 99% VaR), making it more likely to trigger rejection thresholds. **Option C**: **CORRECT** - When using a two-tailed 90% confidence level test for backtesting: - For a 95% VaR model, the expected exception rate is 5% - For a 99% VaR model, the expected exception rate is 1% - The 95% VaR model has a higher expected exception rate, making it less likely to be incorrectly rejected (Type 1 error) because its actual performance is closer to the expected rate **Option D**: Incorrect - Switching to a 99% VaR model doesn't necessarily lower both Type 1 and Type 2 errors. In fact, it may increase Type 2 errors (accepting bad models) because fewer exceptions are expected, making it harder to detect model inadequacy. **Conclusion**: Option C correctly identifies that the 95% VaR model has a smaller probability of incorrect rejection under the specified backtesting conditions due to its higher expected exception rate.
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Q-31. A newly hired risk analyst is backtesting a firm's VaR model. Previously, the firm calculated a 1-day VaR at the 95% confidence level. Following the Basel framework, the risk analyst is recommending that the firm switch to a 99% VaR confidence level. Which of the following statements concerning this switch is correct?
A
The decision to accept or reject a VaR model based on backtesting results at the two-tailed 95% confidence level is less reliable with a 99% VaR model than with a 95% VaR model.
B
The 95% VaR model is less likely to be incorrectly rejected using backtesting than the 99% VaR model.
C
When backtesting using a two-tailed 90% confidence level test, there is a smaller probability of incorrectly rejecting a 95% VaR model than a 99% VaR model.
D
Using a 99% VaR model will lower the probability of committing both type 1 and type 2 errors.